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2 ln(x^2 + 1) + C

5 atan(x) + C

integral de 4x/(x^2+1)

integral de du/u= ln(u) +C

Let be U= X^2 +1 ,so du= 2x

integ(2x/(x^2+1))= integ(u/du)= ln(u)= ln(x^2+1) +C

Integral de 4x/(x^2+1)=

2*integ(2x/(x^2+1)=

***** 2*ln(x^2+1)+C

******************************************

Iintegral de 5/(x^2+1)

x=tgu=(senu/cosu)

d/du tgu= 1+ (tgu)^2

d/du(tan)^(-1)(u) =(1/(tgu)^2+1)

integ[ d/du( tgu)^(-1)

= integral(1/(tgu)^2+1)=integral(1/(x^2+1)

(tgu)^-1= integral (1/(tgu)^2+1)

integral 5/(x^2+1)=

5 integral(1/x^2+1)= 5(tgu)^(-1) +C

= 5tan^(-1)(x) +C

=*****5 arctg(x)+C

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